Answer:
JD is wrong.
Although, the volume of the cube shaped box V' = 421.88 in³ > volume of the sphere V = 268.1 in³, the sphere cannot fit into the box because its diameter, d = 8 in > side of cube = 7.5 in.
Step-by-step explanation:
The sphere would only fit into the cube shaped box if its diameter is less than the length of side of the cube L = 7.5 inches.
So, diameter of sphere d = 2r where r = radius of sphere = 4 inches. Thus, d = 2r = 2(4 in) = 8 in.
Since the diameter of the sphere d = 8 inches > length of side of the cube = 7.5 inches, the sphere would not fit into the box.
So, JD is wrong.
We calculate both the volume of the sphere and cube.
Volume of a sphere V = 4πr³/3 where r = radius of sphere = 4 inches
So, V = 4πr³/3
= 4π(4 in)³/3
= 4π(64) in³/3
= 256π in³/3
= 804.25 in³/3
= 268.1 in³
Volume of a cube V' = L³ where L = length of side of cube = 7.5 inches
So, V' = L³
= (7.5 in)³
= 421.88 in³
Although, the volume of the cube shaped box V' = 421.88 in³ > volume of the sphere V = 268.1 in³, the sphere cannot fit into the box because its diameter, d = 8 in > side of cube = 7.5 in.
